To solve numerically this system of stochastic differential
equations we have used the stochastic second-order Heun method
[1]}, as was previously used in
Refs. [2]}, [3]}. To ensure the effectiveness of the
method we have tested the stability of the solutions and the
convergence of the main magnitudes of this research (average escape
time and energies). Since the Heun method is not a symplectic
algorithm and we have worked with a conservative system, we have
included a negligible amount of dissipation in order to avoid
stability problems in the integration algorithm. We have also
compared the results by using the numerical schemes of the
Euler-Maruyama method and the stochastic fourth-order Runge-Kutta
method [1]}. All the three methods have provided similar
results with a good precision. However, the Heun method has been the
one that offers the best balance between precision and
computational effort.
